Robust Wait Time Estimation in Resource Allocation Systems with an Application to Kidney Allocation

In this paper we study systems that allocate different types of scarce resources to heterogeneous allocatees based on pre-determined priority rules, e.g., the U.S. deceased-donor kidney allocation system or the public housing program. We tackle the problem of estimating the wait time of an allocatee who possesses incomplete system information with regard, for example, to his relative priority, other allocatees’ preferences, and resource availability. We model the system as a multiclass, multiserver queuing system that is potentially unstable or in transient regime. We propose a novel robust optimization solution methodology that builds on the assignment problem. For first-come, first-served systems, our approach yields a mixed-integer programming formulation. For the important case where there is a hierarchy in the resource types, we strengthen our formulation through a drastic variable reduction and also propose a highly scalable heuristic, involving only the solution of a convex optimization problem (usually a second-order cone problem). We back the heuristic with a tight approximation guarantee that becomes tighter for larger problem sizes. We illustrate the generalizability of our approach by studying systems that operate under different priority rules, such as class priority. We conduct a wide range of numerical studies, demonstrating that our approach outperforms simulation.

We showcase how our methodology can be applied to assist patients in the U.S. deceased-donor kidney waitlist. We calibrate our model using detailed historical data to estimate patients’ wait times based on their kidney quality preferences, blood type, location and current rank in the waitlist.